Introduction

The importance of CD4 T-cells in AIDS and HIV infection has long been recognized. Measurements of the CD4 number, obtained from the peripheral blood, give an indication of the amount of immune suppression, with lower numbers indicating more severe immune deficiency. They have been shown to be of great prognostic significance for predicting clinical outcomes (Fahey et al. 1990); they are useful in patient care for monitoring an individual's health; they are used in epidemiological studies and in some countries they are used in determining the availability of health care resources and even are incorporated into the definition of AIDS. CD4 T-cell numbers are also used in determining the eligibility criteria and as stratification variables in randomised clinical trials.

In a previous paper (Taylor et al. 1994) we considered various statistical models which attempted to describe the variation in the patterns of decline of CD4 T-cell numbers in HIV infected subjects. These models were fitted to data from the Los Angeles portion of the Multicenter AIDS cohort study (MACS). One of the aims in this analysis is to investigate whether individuals maintain a fixed rate of decline of CD4 after allowing for the variability of the measurements, that is whether a subject who is following a certain path in their CD4 measurements will remain on that path in the future. One possibility is that individuals do maintain a fixed slope indefinitely, another possibility is that the future slope is unrelated to the past slope. We develop a family of models in which these two scenarios are special cases.